Charged Anisotropic Compact Stars in $f(R,\phi,X)$ Gravity: A Class I Embedding Approach with Reissner-Nordstr\"{o}m Exterior

Abstract

This work examines the physical characteristics of charged, anisotropic compact spheres within the framework of $f(R,\phi,X)$ modified gravity. Starting from a static, spherically symmetric spacetime, we employ an Adler-type ansatz for the temporal metric component $g_{tt}$. The corresponding radial metric component $g_{rr}$ is then systematically derived through application of the Karmarkar condition, which ensures a class-one embedding for the interior geometry. A crucial aspect of our approach involves matching the interior solution at the stellar boundary to the exterior Reissner--Nordstr$\ddot{0}$m spacetime---the established vacuum solution for charged, non-rotating masses. This matching procedure is essential for determining integration constants and verifying global physical consistency. Our comprehensive analysis of the resulting stellar model investigates multiple physical aspects, including energy density, radial and tangential pressures, anisotropy, equation-of-state parameters, energy conditions, mass function, compactness, and surface redshift. Stability assessment further incorporates examination of the adiabatic index and the Tolman--Oppenheimer--Volkoff equation. Collectively, our findings demonstrate that the charged compact star model presented here constitutes a physically viable configuration---free of singularities and maintaining stable equilibrium across the considered parameter space.